Hydrostatic Modeling of the Integrated Soft X‐Ray and Extreme Ultraviolet Emission in Solar Active Regions

Many studies of the solar corona have shown that the observed X-ray luminosity is well correlated with the total unsigned magnetic flux. In this paper we present results from the extensive numerical modeling of active regions observed with the \textit{Solar and Heliospheric Observatory} (\textit{SOHO}) Extreme Ultraviolet Telescope (EIT), the \textit{Yohkoh} Soft X-ray Telescope (SXT), and the \textit{SOHO} Michelson Doppler Imager (MDI). We use potential field extrapolations to compute magnetic field lines and populate these field lines with solutions to the hydrostatic loop equations assuming steady uniform heating. Our volumetric heating rates are of the form $\epsilon_H\sim \bar{B}^\alpha/L^\beta$, where $\bar{B}$ is the magnetic field strength averaged along a field line and $L$ is the loop length. Comparisons between the observed and simulated emission for 26 active regions suggest that coronal heating models that scale as $\epsilon_H\sim \bar{B}/L$ are the most consistent with the observations. These simulations show that the integrated emission is strongly dependent on $\alpha$. Only those heating rates with $\alpha$ close to 1 are consistent with the observed flux-luminosity relationship. We find, however, that the simulated intensities are only weakly dependent on $\beta$ and visualizations of the simulated emission are needed to more fully constrain the simulation results